IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2201.02397.html
   My bibliography  Save this paper

Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance

Author

Listed:
  • Mark Kiermayer
  • Christian Wei{ss}

Abstract

Markov chains play a key role in a vast number of areas, including life insurance mathematics. Standard actuarial quantities as the premium value can be interpreted as compressed, lossy information about the underlying Markov process. We introduce a method to reconstruct the underlying Markov chain given collective information of a portfolio of contracts. Our neural architecture explainably characterizes the process by explicitly providing one-step transition probabilities. Further, we provide an intrinsic, economic model validation to inspect the quality of the information decompression. Lastly, our methodology is successfully tested for a realistic data set of German term life insurance contracts.

Suggested Citation

  • Mark Kiermayer & Christian Wei{ss}, 2022. "Neural calibration of hidden inhomogeneous Markov chains -- Information decompression in life insurance," Papers 2201.02397, arXiv.org.
  • Handle: RePEc:arx:papers:2201.02397
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2201.02397
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Richman, Ronald & Wüthrich, Mario V., 2021. "A neural network extension of the Lee–Carter model to multiple populations," Annals of Actuarial Science, Cambridge University Press, vol. 15(2), pages 346-366, July.
    2. Wu, Sheng-Jhih & Chu, Moody T., 2017. "Markov chains with memory, tensor formulation, and the dynamics of power iteration," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 226-239.
    3. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    4. Mark Kiermayer, 2021. "Modeling surrender risk in life insurance: theoretical and experimental insight," Papers 2101.11590, arXiv.org, revised Aug 2021.
    5. Tobias Burkhart, 2018. "Surrender Risk in the Context of the Quantitative Assessment of Participating Life Insurance Contracts under Solvency II," Risks, MDPI, vol. 6(3), pages 1-38, June.
    6. Philippe Deprez & Pavel V. Shevchenko & Mario V. Wuthrich, 2017. "Machine Learning Techniques for Mortality Modeling," Papers 1705.03396, arXiv.org.
    7. Gabrielli, Andrea, 2020. "A Neural Network Boosted Double Overdispersed Poisson Claims Reserving Model," ASTIN Bulletin, Cambridge University Press, vol. 50(1), pages 25-60, January.
    8. Brecht Verbeken & Marie-Anne Guerry, 2021. "Discrete Time Hybrid Semi-Markov Models in Manpower Planning," Mathematics, MDPI, vol. 9(14), pages 1-13, July.
    9. Blanka Horvath & Aitor Muguruza & Mehdi Tomas, 2021. "Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 11-27, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hung-Tsung Hsiao & Chou-Wen Wang & I.-Chien Liu & Ko-Lun Kung, 2024. "Mortality improvement neural-network models with autoregressive effects," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 49(2), pages 363-383, April.
    2. Basellini, Ugofilippo & Camarda, Carlo Giovanni & Booth, Heather, 2022. "Thirty years on: A review of the Lee-Carter method for forecasting mortality," SocArXiv 8u34d, Center for Open Science.
    3. Heidari , Hassan & Refah-Kahriz, Arash & Hashemi Berenjabadi, Nayyer, 2018. "Dynamic Relationship between Macroeconomic Variables and Stock Return Volatility in Tehran Stock Exchange: Multivariate MS ARMA GARCH Approach," Quarterly Journal of Applied Theories of Economics, Faculty of Economics, Management and Business, University of Tabriz, vol. 5(2), pages 223-250, August.
    4. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    5. Ataurima Arellano, Miguel & Rodríguez, Gabriel, 2020. "Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    6. Chun-Chang Lee & Chih-Min Liang & Hsing-Jung Chou, 2013. "Identifying Taiwan real estate cycle turning points- An application of the multivariate Markov-switching autoregressive Model," Advances in Management and Applied Economics, SCIENPRESS Ltd, vol. 3(2), pages 1-1.
    7. John M. Maheu & Thomas H. McCurdy, 2002. "Nonlinear Features of Realized FX Volatility," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 668-681, November.
    8. Raphaël Homayoun Boroumand & Stéphane Goutte & Simon Porcher & Thomas Porcher, 2014. "A Conditional Markov Regime Switching Model to Study Margins: Application to the French Fuel Retail Markets," Working Papers hal-01090837, HAL.
    9. Avanzi, Benjamin & Taylor, Greg & Wang, Melantha & Wong, Bernard, 2021. "SynthETIC: An individual insurance claim simulator with feature control," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 296-308.
    10. Aloui, Chaker & Hammoudeh, Shawkat & Hamida, Hela Ben, 2015. "Price discovery and regime shift behavior in the relationship between sharia stocks and sukuk: A two-state Markov switching analysis," Pacific-Basin Finance Journal, Elsevier, vol. 34(C), pages 121-135.
    11. Liu, Yue & Sun, Huaping & Zhang, Jijian & Taghizadeh-Hesary, Farhad, 2020. "Detection of volatility regime-switching for crude oil price modeling and forecasting," Resources Policy, Elsevier, vol. 69(C).
    12. Alistair Mees & Berndt Pilgram, 2000. "Non-Linear Markov Modelling Using Canonical Variate Analysis: Forecasting Exchange Rate Volatility," Econometric Society World Congress 2000 Contributed Papers 1162, Econometric Society.
    13. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    14. Charlotte Christiansen, 2004. "Regime switching in the yield curve," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(4), pages 315-336, April.
    15. Patrick Büchel & Michael Kratochwil & Maximilian Nagl & Daniel Rösch, 2022. "Deep calibration of financial models: turning theory into practice," Review of Derivatives Research, Springer, vol. 25(2), pages 109-136, July.
    16. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    17. Marcin Chlebus, 2016. "Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?," FindEcon Chapters: Forecasting Financial Markets and Economic Decision-Making, in: Magdalena Osińska (ed.), Statistical Review, vol. 63, 2016, 3, edition 1, volume 63, chapter 4, pages 329-350, University of Lodz.
    18. repec:ipg:wpaper:2014-552 is not listed on IDEAS
    19. Soo Khoon Goh & Guay Lim & Nilss Olekalns, 2006. "Deviations from uncovered interest parity in Malaysia," Applied Financial Economics, Taylor & Francis Journals, vol. 16(10), pages 745-759.
    20. Choi Seungmoon, 2009. "Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-41, March.
    21. Eduardo Abi Jaber & Shaun & Li, 2024. "Volatility models in practice: Rough, Path-dependent or Markovian?," Papers 2401.03345, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2201.02397. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.